Charge-carrier deep-trapping kinetics in high-resistivity semiconductors

The Kanazawa-Batra formulation of deep-trapping kinetics in high-resistivity semiconductors is reformulated to obtain a general differential equation that describes the instantaneous electric field E(x, t) in a solid in which charge transport and trapping occurs in the presence of discrete levels of deep traps. The model developed herein specifically takes into account that, as deep trapping proceeds, the concentration of empty traps decreases due to trap filling. The latter effect was ignored in previous models. Furthermore, the possibility of release from deep traps is also included. A second-order nonlinear partial differential equation is obtained for E(x, t) which fully describes the deep trapping kinetics in a high-resistivity solid. The numerical solution of this differential equation for a photo-induced discharge (PID) process, with a field-dependent photo-injection mechanism, gives the instantaneous and the final electric fields in the sample and hence the time evolution of the surface voltage and the residual surface potential as a function of charge transport and trapping parameters. The relationship between the xerographic residual potential and the mobility-lifetime product (charge-carrier range) is examined and discussed in terms of charge transport and trapping parameters in high-resistivity solids, and a-Si:H is considered as an example. The present formulation of deep-trapping kinetics puts a limitation on the interpretation of xerographic residual-voltage experiments and moreover emphasizes the need for other collaborating experiments for a meaningful evaluation of trap parameters.